# Radiation dynamics in fast soliton collisions in the presence of cubic loss

## TL;DR

This paper investigates radiation emission during fast soliton collisions in the nonlinear Schrödinger equation with weak cubic loss, using perturbation theory and numerical simulations to understand the dynamics and effects of nonlinearity.

## Contribution

It extends perturbation techniques to analyze radiation dynamics in dissipative soliton collisions, demonstrating good agreement with numerical results across various parameters.

## Key findings

- Perturbation theory accurately predicts radiation emission for large group velocity differences.
- Numerical simulations confirm the validity of the perturbation approach.
- Kerr nonlinearity influences interpulse interactions at intermediate velocities.

## Abstract

We study the dynamics of emission of radiation (small-amplitude waves) in fast collisions between two solitons of the nonlinear Schr\"odinger (NLS) equation in the presence of weak cubic loss. We calculate the radiation dynamics by a perturbation technique with two small parameters: the cubic loss coefficient $\epsilon_{3}$ and the reciprocal of the group velocity difference $1/\beta$. The agreement between the perturbation theory predictions and the results of numerical simulations with the full coupled-NLS propagation model is very good for large $\beta$ values, and is good for intermediate $\beta$ values. Additional numerical simulations with four simplified NLS models show that the differences between perturbation theory and simulations for intermediate $\beta$ values are due to the effects of Kerr nonlinearity on interpulse interaction in the collision. Thus, our study demonstrates that the perturbation technique that was originally developed to study radiation dynamics in fast soliton collisions in the presence of conservative perturbations can also be employed for soliton collisions in the presence of dissipative perturbations.